They would be a solution if almost all parents used them, but parents don't want to socially isolate their kids since a lot of "social" activity is now on social media. It's kind of a prisoner's dilemma.
There's not necessarily wrong. Despite the vapid and damaging nature of most popular online media, isolating a child from it might have even worse social consequences when their real-life peer groups discover that they're not on social media or that their parents have neutered their phone. Some kids would turn out fine after that. Others would be socially destroyed for life (maybe with the right therapy they could become well-adjusted, but high quality therapy is rare).
I should not have to surrender my anonymity because parents are too lazy to setup parental controls.
Parental controls can set browsers in "child mode" where the browser sends an "I am a child" header to the server and social networks etc. need to honour it. This has existed for twelve years already: https://blog.mozilla.org/netpolicy/2014/07/22/prefersafe-mak... . It can probably be amended with a more granular set of levels, but that would be the best way forward.
The problem of "parents are negligent" is also solved by existing laws which have fines for parents who are negligent towards their children, and governments absolutely love collecting fines, so all the incentives are properly aligned.
> They would be a solution if almost all parents used them
No, they are a solution for parents who want to use them, and that's all they should be. Their existence demonstrates that it's possible to handle this without regulation, other than the desire of some people to inflict their preferences onto other people's kids.